Electric filter network



Dec. 8, 1953 E J. F. KLINKHAMER 2,662,216

ELECTRIC FILTER NETWORK Filed May 16. 1950 2 Sheets-Sheet l INVENTOIL JACOB FREDRIK KLINKHAMER AGENT Dec. 8, i953 J. F. KLINKHAMER 2,662,216

ELECTRICA4 FILTER NETWORK Filed May 16, 1950 l 2 sheets-snee*b 2 JACOB FREDRIK KLINKHAMER BY www AGENT Patented Dec. 8, 1953 ELECTRIC FILTER NETWORK Jacob Fredrik Klinkhamer, Eindhoven, Netherlands, assigner to Hartford National Bank and Trust Company, Hartford, Conn., as trustee Application May 16, 1950, Serial No. 162,296

Claims priority, application Netherlands June 1, 1949 (Cl. S33-70) 5 Claims.

The present invention relates to ladder networks and more particularly to ladder networks comprising at least two sections and having a straight transmission characteristic curve which drops abruptly towards zero outside the transmission band of the network. The term section is to be understood to mean the parts of which the network is built up and each of which comprises an impedance in the series circuit followed by an impedance in the parallel circuit of the network. The term section impedance is to be understood to mean the series or the parallel impedance respectively of said section.

The principal object of the present invention is to provide a ladder network with improved transmission characteristic.

4Another object of the invention is to provide a ladder network wherein the use of substantially pure reactance elements is not necessary to achieve good characteristics.

Further objects of the invention will appear from the following description.

Network theorists have devised a network synthesis which permits to calculate the value of the section impedances of such a network, for example a band-pass filter network. For this purpose the desired transmission characteristic curve is written in an algebraic form of a broken, rational polynomial in the complex frequency A, the roots of the numerator of this polynomial corresponding to the zero points and those oi the denominator corresponding to the poles of the transmission characteristic curve of the network. If the network is constituted by loss-free reactances, the zero points are all purely imaginary. The values of the reactances may then be directly determined according to any of the known syntheses. En general, the calculation is carried on on the assumption that the energy absorption, which is caused by the loss components of the network reactance elements is negligible relative to that of an input and/ or output resistance. ln order that this assumption may be permissible and the network not absorb an excessive amount of energy, the reactances should have low losses.

The manufacture of reactances suinciently free from losses is, however, comparatively costly so that there will always be a tendency to build up the network from reactances which are not free from losses. For determining the values of these reactances the network synthesis hitherto e.- ployed did not provide a general solution.

The invention is based on the recognition that, in constructing a network to have a desired transmission characteristic, only a slight error is made put resistance so that the network has substana complex frequency \'=i|-Hn, so that all the poles and Zero points are increased by the same real value -Ho. The physical significance of this is that, loss resistances having a value HOL and are introduced in series with the induotances L and in parallel with the condensers C respectively. It is now found that the transmission characteristic curve of such a network substantially coincides with that of the basic network, except that.- in the neighbourhood of the limiting or cutoff frequencies, the transmission characteristic curve exhibits irregularities; it appears namely that, at these frequencies, the transmission is higher or the attenuation, i. e. the negative logarithm of the transmission is lower than it should be both within and without the transmission band. The invention is intended to provide a network comprising reactances which are not free from losses, but in which these irregularities are avoided.

The invention is characterized in that the poles and zero points of the desired network, which is constituted by reactances having loss components and an input and/or an output resistance, correspond to that of a network consisting of loss-free reactances, and an input and/or an outtially the same transmission characteristic curve as a network comprising loss free reactance elements; the zero points of the desired network, compared to those ofthe basic network, are increased by the same real amount -Ho, and in the network thus obtained, that section which is associated with at least one of the two zero points of this network outside of but the most adjacent to the transmission band, is replaced by a section having the same impedance but which does not pass the frequencies in the proximity of the zero point.

For the section to be made free from losses a final sectionpof the network will preferably be chosen, in which event only the input impedance of the substitute section need be equal tc that of the initial section.

In order that the invention may be more clearly understood and readily carried into effect, it will now be described in detail withY reference. to the accompanying drawing, in which:

Fig. l shows a known basic ladder network,

Fig. 2 shows the characteristic transmission. and attenuation curves of this basic network and' of the network corresponding theretoafter alli the zero points have been increasedrby thasamc real value or damping factor -Ht-.

Fig. 3 shows the poles and the zero pointsof the transmission function of; theV network.V

Fig. 4 shows the poles and thezero points ofv an input admittance of the final section ofthe net.- work in the complex w-plane,

Fig. 5 is a diagram of this iinal section modiiied according to the invention, and

Fig. 6 shows another embodimentof this final section according to the invention.

Referring now to the drawing, Fig. 1` shows a ladder network having a large numberr of sections and a straight transmission characteristic curve which drops abruptly toward zero outside the transmission band of the network.. Thiszmay be, for example, a band-pass filter network` with a band-pass characteristic as represented. by curve a in Fig. 2'. The attenuation of this network, i. e. the negative logarithm of the; transmission as a function ofthe frequency, is' indicatedV by curve b-c-d-e--f-g-u In order to calculate the' impedance values. of the section impedances of this network according to the method hitherto used, all the losses of these impedances are assumed negligible as compared with those of a final resistance, for eX- ample an input'resistance I. In this4 event, after separating this input resistance, theA remaining network, ofv which the poles Pf and the zero points 0 are all located on the w axis, consists oi'f lossfree reactances, the values of' which can bedetermined by any'of the known network syntheses.

To ensure the desired transmission characteristic curve, these reactances of the network must be constructed so as to be asfree from losses as possible. Reactances of this character are, however, expensive, so that a network so-constructed would be expensive'.

According to the invention, this difficulty is avoided as follows. Instead of usingl the network obtained which, the input resistance lf inclusive, exhibits as an example the poles P1 and the zero points 01, the values of the reactances are determined, by the'method hitherto used, for a network having the same zero points 02, but all poles P2 of which are shifted by an equal amount Ho from the w axis. This network in itself will not Y exhibit the desired transmission characteristic curve, but by' replacing y'wvby fc4-Hc in all. reactance values y'wL and L or in parallel with each calculated capacity C,

respectively. These resistance values may be the natural loss resistances ofthek reactance elements. `75

It has been found that this transmission characteristic curve exhibits irregularities only in the neighbourhood of the limiting or cut-off frequencies m and n, i. e. within the transmission band the network is found to have too low attenuation in. this neighbourhood as compared withthe further ranger so that an attenuation, characteristic similar to the curve b--c-p--e--q--g-h is obtained.

If it should be endeavoured to obviate this too l'cwy attenuation by additional damping of a circutaof thenetwork having a resonance frequency i'rr theneighbourhood of, say, the upper cut off frequency/11.', a characteristic curve is obtained correspondingto curve b-c-p-e-f-r-h. The attenuation outside the transmission band decreases, as can be seen from part 1' of the characteristic curves.

Particularly at the higher cut-off frequency n this may be objectionable. As appears from the frequencyv values shown. byxway of example,` the frequency difference required in order to obtain a prescribed attenuation is usually smaller at the lower cut-offV frequencym than at the higher cutoi frequency n. Particularly on the side of the higher cut-oif frequency special precautions must be taken to obviate undue irregularities without causing the peak g in the attenuation characteristic curve, to disappear.

Thisisachieved byv replacing the sectionv of the network associated with the zero point nearest the cut-off frequency n, by a section which does not pass the frequencies associated with this zero point, care being taken that both the input and the oiitputy impedances of the section concerned are not Varied, in order that the further characteristic curve ofthe network is not affected. These input andv output i hpedances have fixed values, since the reactances are determined in accordance with the foregoing. 'The characteristic curve of the. network at the cut-oi frequency n then becomes c-f-s-h.

The invention. will be explained particularly for the case in which the nal section 2 of the network of Fig. l is chosen as the section to be replaced'. As stated above, the reactances 3, d and 5 of this section, which are not free from losses, have fixed Values, since their purely reactiveI component has been found as the result of a known method of calculation of the network with zero pointsy 02 and poles P2. The loss resistances ofj these reactance elements. which in the case of inductance, may be a series resistance and, in the case of capacitors, a parallel resistance, has been found to be Il@ times these inductance and capacity values respectively. Thus, the input impedance of this section is known. Its converse, the input admittance which is therefore also known, may be:

where A, H0, a and b are constants determined bythe calculation indicated above. This admittance exhibits poles P and zero points 0, as shown in the complex A-plane 0f Fig. 4, where H represents the real (damping) and w represents the imaginary (frequency) components of A. Section 2 produces a. zero point in the transmission characteristic curve of the network, since the circuit 3--d, corresponding to the aditional complex points (h2 and 0'12 constitutes, at its resonance frequency, a high impedance relative to capacitor 5. `The ladder network is here broken olf up to. the said sections such that, of all the network zero points, the zero point concerned approaches most closely the ransmission passage band of the network.

This section is now replaced by such a section that frequencies in the proximity of the zero point U12 are no longer allowed to pass, the reactanceand resistance values of the section formerly found varying, but the input admittance Y remaining unchanged. This is achieved. as follows. ance R1 in the series branch is followed by a resistance R2 in the parallel branch as shown in Fig. 5. The values of the elements are given by the equations:

2b2A 1. Crit cvsweb@ Eil-inc,I Rianofic,

The admittance of the remaining portion of the section, if H0 is assumed to be small, assumes the form:

where n2=b2QHu2 corresponds to the zero points 012, 012 of the admittance of the section. This remainingadmittance may furthermore be reduced, in regard to frequencies of the transmission band of the network, to a parallel resonance circuit LzCz in the series branch and a capacitor C3 with loss resistance R3 in the parallel branch of the network, the values of which are:

Instead of a network of which all reactances are required to have very low losses, a network is thus obtained in which only the circuit L2C2 must have very low losses. This network still yields the favourable attenuation characteristic curve b-c-d-e-f-g-h. However, this requirement concerning the circuit LzCz may furthermore be avoided by applying a Norton transformation to the section part Rz-Cz-Lz-Ra of the network.

In this event the resistances R2 and Rs are While I have described my invention in a specic use thereof and in specific embodiments, I do not wish to be limited thereto, for obvious modifications will occur to those skilled in the art without departing from the spirit and scope of the invention.

First of all a capacitor C1 with loss resistf What I claim is:

1. A ladder network having a transmission characteristic function whose poles and zeros correspond to a characteristic curve which is substantially rectilinear for frequencies falling within a selected frequency band and which abruptly drops toward zero for frequencies falling outside of said band, said network comprising a plurality of sections each of which is provided with reactance elements and inherent loss resistances, said reactances and resistances having values at which the frequencies determined by the poles cf the characteristic function of said ladder network are equal to the frequencies determined by the poles of an idealized network having a like plurality of sections provided with loss-free reactanoe elements and having a transmission characteristic curve substantially equal to that of said ladder network, said resistances having values at which the frecnienciesA determined by the zeros of the characteristic curve of said ladder network differ by a constant imaginary amount from the frequencies determined by the zeros of said idealized network, one section of the nonideal ladder network having a zero which determines that frequency which falls outside of and is most adjacent to said band including reactance elements preventing transmission of said outside frequency.

2. A ladder network as set forth in claim 1 wherein said one section whose zero determines said outside frequency is a terminal section of said non-ideal network.

3. A ladder network as set forth in claim l wherein said one section is a terminal section of the non-ideal network and has an impedance value equal to that of the corresponding section of the ideal network.

4. A network, as set forth in claim 1, wherein said one section is a terminal section and includes a pair of input and a pair of output terminals, one input and one output terminal being interconnected, a resistance-capacitance parallel circuit and a resistance-inductance parallel circuit serially connected between the other input and output terminals, a resistance-capacitance parallel circuit connected across said output terminals, and a resistor connected between the junction of the serially connected parallel circuits and the interconnection of said other input and output terminals.

5. A network, as set forth in claim 1, wherein said one section is a terminal section including a pair of input and aY pair of output terminals, one input terminal and one output terminal being interconnected, a resistance-capacitance parallel circuit and resistance-capacitance-inductance parallel circuit connected serially between the other input and output terminals, a capacitor connected across said output terminals, and a resistor connected between a point in said inductance and the other interconnected terminals.

JACOB FREDRIK KLINKHAMER.

References Cited in the le of this patent UNITED STATES PATENTS Number Name Date 1,850,146 Zobel Mar. 22, 1932 2,093,665 Tellegen Sept. 21, 1937 2,342,638 Bode Feb. 29, 1944 

